Related papers: Recherches autour de la theorie de Markoff
Recent developments in the theory of stability conditions and its relation to Teichmuller theory have revealed a deep connection between triangulated categories and surfaces. Motivated by this, we prove a categorical analogue of the…
In this expository note, I present some of the key features of the lattice of torsion classes of a finite-dimensional algebra, focussing in particular on its complete semidistributivity and consequences thereof. This is intended to serve as…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
We derive a closed-form expression for all genus 1 Hurwitz numbers, and give a simple new graph-theoretic interpretation of Hurwitz numbers in genus 0 and 1. (Hurwitz numbers essentially count irreducible genus g covers of the sphere, with…
Approximation theory is a substantial field of mathematical analysis that emerged in the 19th century and has been developed by mathematicians across the globe ever since. Its importance has increased over time, as it provides solutions to…
We suggest a generalization of \pi_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of…
With the aim of understanding compactifications of 6D superconformal field theories to four dimensions, we study punctures for theories of class $\mathcal{S}_{\Gamma}$. The class $\mathcal{S}_{\Gamma}$ theories arise from M5-branes probing…
We provide a construction which covers as special cases many of the topologies on integers one can find in the literature. Moreover, our analysis of the Golomb and Kirch topologies inserts them in a family of connected, Hausdorff topologies…
We survey two decades of work on the (sequential) topological complexity of configuration spaces of graphs (ordered and unordered), aiming to give an account that is unifying, elementary, and self-contained. We discuss the traditional…
In this thesis we investigate a new formalism for supergeometry which focuses on the categorical properties of the theory. This approach is our main tool in the subsequent investigation of a global analytic approach to the construction of…
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…
The punctured solenoid $\S$ is an initial object for the category of punctured surfaces with morphisms given by finite covers branched only over the punctures. The (decorated) Teichm\"uller space of $\S$ is introduced, studied, and found to…
Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…
There is a need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept…
We provide geometrical interpretation of the Master Theorem to solve divide-and-conquer recurrences. We show how different cases of the recurrences correspond to different kinds of fractal images. Fractal dimension and Hausdorff measure are…
This paper, together with a forthcoming paper by the author and Seitz, proves the Margulis-Platonov conjecture concerning the normal subgroup structure of algebraic groups over number fields, in the case of inner forms of anisotropic groups…
The aim of these lecture notes is, after having quickly described various compactifications of the Teichm\"{u}ller space of a compact connected oriented surface minus finitely many points, to give a construction, by the equivariant Gromov…
Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1|1) model of Rozansky and Saleur on $\Sigma x S^{1}$, both directly and using equivalent two-dimensional…
State-of-the-art algorithms in lattice gauge theory typically rely heavily on detailed balance, which is an instrumental tool to prove the correct convergence of the Markov Chain Monte Carlo Algorithm. In this work, we investigate an…
The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the well-known ordinary calculus is being used extensively in many fields, particularly in…